Import Question JSON

Current Question (ID: 20301)

Question:

$\text{Eight copper wire of length } l \text{ and diameter } d \text{ are joined in parallel to form a single composite conductor of resistance } R. \text{ If a single copper wire of length } 2l \text{ have the same resistance } (R) \text{ then its diameter will be:}$

Options:

1. $4d$
2. $3d$
3. $2d$
4. $d$

Solution:

$\text{Hint: } R = \rho \frac{l}{A}$ $\text{Step: Find the diameter of the copper wire.}$ $R = \frac{1}{8} \left( \frac{\rho l \times 4}{\pi d^2} \right) = \frac{\rho \times 2l \times 4}{\pi \times d'^2}$ $d'^2 = 16d^2$ $d' = 4d$ $\text{Option (1) is correct.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}